Arrayed waveguide grating based modular interconnection networks and methods for constructing and applying the same

ABSTRACT

An arrayed waveguide grating (AWG) based interconnection network and modular construction method, comprising N 1  left nodes, with each left node having N 2  ports, N 2  right nodes, with each right node having N 1  ports, where N 1 ≧N 2 , N 1  and N 2  having a greatest common divisor r, and each port having an optical transceiver associated with a fixed wavelength; N 1 n 2  r×1 wavelength multiplexers having their input ports respectively connected with the ports of N 1  left nodes, where n 2 =N 2 /r; N 2 n 1  1×r wavelength demultiplexers having their output ports respectively connected with the ports of N 2  right nodes, where n 1 =N 1 /r; n 1 n 2  r×r AWGs connecting the r×1 wavelength multiplexers and the 1×r wavelength demultiplexers r×rn 1 n 2 , and each of the r×r AWGs being associated with a wavelength subset {λ k |k=0, 1, . . . , r−1}.

CROSS-REFERENCE AND RELATED APPLICATIONS

The subject application claims priority on Chinese patent application No. CN 201410410122.8 filed on Aug. 20, 2014. The contents and subject matter of the Chinese priority application is incorporated herein by reference.

FIELD OF TECHNOLOGY

The present invention relates to large-scale networking of a data center, and in particular, relates to an arrayed waveguide grating (AWG) based modular interconnection network and methods for constructing and applying the same.

BACKGROUND OF THE INVENTION

In the past decade, fast global information development push data centers to evolve along the direction of super large scale. In 2012, each data center of Amazon has about 60,000 servers, and that for Google, the number exceeds 50,000 servers, while Microsoft is building a data center containing over 300,000 servers. Current data centers generally adopt the layered tree topology, such as the ‘Fat Tree’ topology. The advantage of the tree topology is its large bi-directional bandwidth, while the disadvantage is its lack of scalability. As pointed out in the Article entitled “60 GHz Data-Center Networking: Wireless

Worry less,” topological and cabling complexity in data centers is reaching unimaginable proportions, leading to maintenance challenges, inefficient cooling, and substantial operational costs.

To tackle the interconnecting issue, the following proposals have been put forth in the industry:

The first is to replace wires with wireless interconnects. Wireless networking has signals prone to interference, small bandwidth, and high consumption of stations, making it only a topic at the academies, and not fit for practical application.

The second is to develop a unified structure based on integrated and enhanced Ethernets, with Cisco and Brocade being the major proponents. Although the method decreases the number of cables, trunk adapters, and network interfaces, the cost of equipping and integrating network adapters is huge, further, main boards for Ethernet optical fiber channels are not yet available.

The third is to adopt structured cabling. The main idea is to divide the cabling system in a data center into a main cabling area and a device area based on different devices. The main cabling area and the device area are connected with optical cables, while servers, switchers, and storage devices are jumper-connected via cable distribution frames in the main cabling area and the device area. The proposed solution simplifies cable management to some extent, making it possible to move or modify the system by merely changing jumpers. But it does not decrease the number of system cables, thus interconnecting complexity remains and the operating difficulty is still high.

Because of the above reasons, a method of module networking based on Arrayed Waveguide Grating (AWG) and directed at cabling complexity and management in a data center is in need.

SUMMARY OF THE INVENTION

The present invention solves the problem of the cabling complexity and related management issues by providing a design method of AWG-based modular interconnection networks to reduce cabling complexity so as to simplify networking maintenance and management.

The present invention provides an AWG-based modular interconnection network comprising left nodes, the number of the left nodes being N₁, with each left node having N₂ ports; right nodes, the number of the right nodes being N₂, with each right node having N₁ ports; N₁ and N₂ each representing a positive integer, N₁≧N₂, and N₁ and N₂ having a greatest common divisor r, and each port having an optical transceiver associated with a fixed wavelength, characterized in that it further comprises:

N₂×1 wavelength multiplexers, the number of the N₂×1 wavelength multiplexers being N₁, with each of the N₂×1 wavelength multiplexers having N₂ input ports being respectively connected with the N₂ ports of each of the left nodes;

1×N₁ wavelength demultiplexers, the number of the 1×N₁ wavelength demultiplexers being N₂, with each of the 1×N₁ wavelength demultiplexers having N₁ output ports respectively connected with the N₁ ports of each of the right nodes; and

an N₁×N₂ AWG connecting the N₂×1 wavelength multiplexers and the 1×N₁ wavelength demultiplexers, the N₁×N₂ AWG having N₁ input ports and N₂ output ports, and being associated with a wavelength set Λ={λ₀, λ₁, . . . , λ_(N) ₁ ⁻¹}.

The present invention further provides an AWG-based modular interconnection network, comprising left nodes, the number of the left nodes being N₁, with each of the left nodes having N₂ ports, right nodes, the number of the right nodes being N₂, with each of the right nodes having N₁ ports; N₁ and N₂ are integers, N₁≧N₂, N₁ and N₂ having the greatest common divisor r, and each port having an optical transceiver associated with a fixed wavelength, characterized in that it further comprises:

r×1 wavelength multiplexers, the number of the r×1 wavelength multiplexers being N₁n₂ (N₁n₂ stands for the product of N₁ and n₂, and same goes for the same styled numbers in the subject application), and n₂ r×1 wavelength multiplexers having their input ports respectively connected with the N₂ ports of one of the left nodes, where n₂=N₂/r;

1×r wavelength demultiplexers, the number of the 1×r wavelength demultiplexers being N₂n₁, and n₁ 1×r wavelength demultiplexers having output ports respectively connected with the N₁ ports of one of the right nodes, where n₁=N₁/r; and

r×r AWGs connecting the r×1 wavelength multiplexers and the 1×r wavelength demultiplexers, the number of the r×r AWGs being n₁n₂, and each of the r×r AWGs being associated with a wavelength subset {λ_(k)|k=0, 1, . . . , r−1}.

The present invention also provides an AWG-based modular interconnection network, comprising left nodes, the number of the left nodes being N₁, with each of the left nodes having N₂ ports; right nodes, the number of the right nodes being N₂ with each of the right node having N₁ ports; N₁, N₂, and K are integers, where N₁=KN₂; and each port having an optical transceiver associated with a fixed wavelength, characterized in that it further comprises:

N₂×1 wavelength multiplexers, the number of the N₂×1 wavelength multiplexers being N₁, each of the N₂×1 wavelength multiplexers having N₂ input ports respectively connected with the N₂ ports of each of the left nodes;

1×N₂ wavelength demultiplexers, the number of the 1×N₂ wavelength demultiplexers being KN₂, the K 1×N₂ wavelength demultiplexers having their output ports respectively connected with the N₁ ports of one of the right nodes; and

N₂×N₂ AWGs connecting the N₂×1 wavelength multiplexers and the 1×N₂ wavelength demultiplexers, the number of the N₂×N₂ AWGs being K, each of the N₂×N₂ AWGs being associated with a wavelength subset {λ_(k)|k=0, 1, . . . , N₂−1}.

The present invention further provides a method for constructing an AWG-based modular interconnection network having N₁ left nodes, with each left node having N₂ ports; the N₂ right nodes, with each right node having N₁ ports; N₁≧N₂, N₁ and N₂ being integers having a greatest common divisor r; and each port having an optical transceiver associated with a fixed wavelength, characterized in that the method comprises the following steps:

Step 1: providing N₁ N₂×1 wavelength multiplexers, labeled by L₀, L₁, . . . , L_(N) ₁ ⁻¹, for the N₁ left nodes, the ith N₂×1 wavelength multiplexer having its jth input port connected with the jth port of the ith left node, and the jth port of the ith left node is associated with wavelength

λ_([i + j]_(N₁)), where i=0, 1, . . . , N₁−1, j=0, 1, . . . , N₂−1;

Step 2: providing N₂ 1×N₁ wavelength demultiplexers labeled by R₀, R₁, . . . , R_(N) ₂ ⁻¹, for N₂ right nodes, the jth 1×N₁ wavelength demultiplexer having its ith output port connected separately with the ith port of the jth right node, and the ith port of the jth right node is associated with wavelength

λ_([i + j]_(N₁));

Step 3: interconnecting the N₁ wavelength multiplexers on the left with the N₂ wavelength demultiplexers on the right via an N₁×N₂ AWG, the N₁×N₂ AWG having N₁ input ports and N₂ output ports, and being associated with a wavelength set Λ={λ₀, λ₁, . . . , λ_(N) ₁ ⁻¹}.

The method further comprises:

Step 4: substituting the N₁×N₂ AWG with a three-stage AWG network S_(A)(n₁,r₁,m_(A),n₂,r₂), the AWG network S_(A) comprising N₁=r₁n₁ input ports on its input side, with each input port being a 1×n₂ wavelength demultiplexer, and N₂=r₂n₂ output ports on its output side, with each output port being an n₁×1 wavelength multiplexer, m_(A) r₁×r₂ AWGs in the central stage, where r₁=r₂=r, n₁=N₁/r, n₂=N₂/r, and m_(A)=n₁n₂;

In the AWG network S_(A), the ith input port is labeled by D_(A1)(α_(A),a_(A)), where α_(A)=└i/n₁┘ and α_(A)=[i]_(n) ₁ , and the jth output port is labeled by M_(A1)(β_(A),b_(A)), where β_(A)└j/n₂┘ and b_(A)=[j]_(n) ₂ , and each of the AWGs in the central stage is labeled by G_(A1)(α_(A),b_(A)); the α_(A)th input port of G_(A1)(α_(A),b_(A)) is connected with the b_(A)th output port of D_(A1)(α_(A),a_(A)), the β_(A) th output port of G_(A1)(α_(A),b_(A)) is connected with the α_(A)th input port of M_(A1)(β_(A),b_(A)), and G_(A1)(α_(A),b_(A)) is associated with a wavelength subset Λ_([α) _(λ) _(+b) _(λ) _(]) _(n1) ={λ_([α) _(λ) _(+b) _(λ) _(]) _(n1) _(r+k)|k=0, 1, . . . , r−1};

Step 5: substituting the ith N₂×1 wavelength multiplexer L_(i) and the 1×n₂ wavelength demultiplexer D_(A1)(α_(A),a_(A)) with n₂ r×1 wavelength multiplexers, each of which is labeled by D_(A2)(α_(A),a_(A),b_(A));

substituting the jth 1×N₁ wavelength demultiplexer R_(j) and the n₁×1 wavelength multiplexer M_(A1)(β_(A),b_(A)) with n r×1 wavelength demultiplexers, each of the r×1 wavelength demultiplexers being labeled by M_(A2)(β_(A),b_(A),a_(A));

associating each r₁×r₂ AWG, labeled by D_(A2)(α_(A),b_(A)), with a wavelength subset (λ_(k)|k=0, 1, . . . , r−1);

where the output port of D_(A2)(α_(A),a_(A),b_(A)) is connected with the α_(A)th input port of G_(A2)(a_(A),b_(A)), and the input port of M_(A2)(β_(A),b_(A),a_(A)) is connected with the β_(A)th output port of G_(A2)(α_(A),b_(A)).

Alternatively, the method further comprises:

Step 4: in the case of N₁=KN₂, substituting the N₁×N₂ AWG with a two-stage network S_(B)(K,N₂,K,1,N₂), where each input port of the AWG network S_(B) is a link, there are K N₂×N₂ AWGs in the central stage, and each output port is a K×1 wavelength multiplexer; the ith input port is labeled by D_(B1)(α_(B),a_(B)), where α_(B)=└i/N₂┘ and a_(B)=[i]_(N) ₂ , the jth output port is labeled by M_(B1)(γ_(B)), where γ_(B)=j, and each AWG in the central stage is labeled by G_(B1)(α_(B)), and further, the AWG in the central stage is associated with a wavelength subset Λ_(α) _(B) ={λ_(α) _(B) _(N) ₂ _(+k)|k=0, 1, . . . , N₂−1}; the a_(B)th input port of G_(B1)(α_(B)) is thus D_(B1)(α_(B),a_(B)), the γ_(B)th output port of G_(B1)(α_(B)) is connected with the α_(B)th input port of M_(B1)(γ_(B));

Step 5: denoting each of the N₁×1 wavelength multiplexers as D_(B2)(α_(B),a_(B));

Substituting the jth 1×N₁ demultiplexer R_(j) and the K×1 multiplexer M_(B1)(γ_(B)) with K N₂×1 wavelength multiplexers, each of which is labeled by M_(B2)(γ_(B),α_(B));

associating each N₂×N₂ AWG, labeled by G_(B2)(α_(B)), with a wavelength subset {λ_(k)|k=0, 1, . . . , N₂−1};

where D_(B2)(α_(B),a_(B)) is connected with the a_(B)th input port of G_(B2)(α_(B)), and M_(B2)(γ_(B),α_(B)) is connected with the γ_(B)th output port of G_(B2)(α_(B)).

The method further comprises:

Step 6: in the case of the dimension of the AWG in the central stage still being large, returning to Step 4, and substituting the AWG in the central stage with a module constituted of a three-stage network of small AWGs.

The present invention further provides an application of AWGs in an interconnection network. Compared with the previous works, the present invention has the following advantages:

(1) By constructing the N₁×N₂ interconnection network with the r×r AWGs, the number of the interconnection links is reduced r times.

(2) Wavelengths are reused in the AWG-based interconnection network, i.e., the r×r AWGs in the network reuses the same wavelength subset {λ₀, . . . , λ_(r−1)}, which improves the scalability of the AWG-based interconnection system.

(3) If r is still very large, the method in Step 4 can be employed to decompose the r×r AWG into an r×r three-stage AWG network.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an N₁×N₂ interconnection network

₁ of the present invention;

FIG. 2 shows an AWG-based N₁×N₂ interconnection network

₂ of the present invention;

FIG. 3 shows an N₁×N₂ interconnection network

_(A1) comprising a three-stage AWG network S_(A) of the present invention;

FIG. 4 shows a KN₂×N₂ interconnection network

_(B1) comprising a two-stage AWG network S_(B) of the present invention;

FIG. 5 shows an N₁×N₂ AWG-based modular interconnection network

_(A2) of the present invention;

FIG. 6 shows a KN₂×N₂ AWG-based modular interconnection network

_(B2) of the present invention;

FIG. 7 shows a 15×10 interconnection network

₁ of the present invention;

FIG. 8 shows a 15×10 AWG-based interconnection network

₂ of the present invention;

FIG. 9 shows a 15×10 interconnection network

_(A1) comprising an AWG network S_(A) of the present invention;

FIG. 10 shows a 15×10 AWG-based modular interconnection network

_(A2) of the present invention;

FIG. 11 shows a 12×6 interconnection network

₁ of the present invention;

FIG. 12 shows a 12×6 AWG-based interconnection network

₂ of the present invention;

FIG. 13 shows a 12×6 AWG-based interconnection network

_(B1) comprising a two-stage AWG network S_(B) of the present invention;

FIG. 14 shows a 12×6 AWG-based modular interconnection network

_(B2) of the present invention.

DETAILED DESCRIPTION OF THE INVENTION AND PREFERRED EMBODIMENTS

In combination with drawings and embodiments hereunder provided, the present invention will be further expounded. The embodiments are intended as illustrating the present invention rather than limiting its scope. Various equivalent modifications by a person skilled in the art shall fall within the scope of the claims.

An N₁×N₂ (N₁≧N₂, and N₁ and N₂ having a maximum divisor r) interconnection network

₁ contains N₁ left nodes, with each node comprising N₂ ports, and each port having an optical transceiver; N₂ right nodes, with each node comprising N₁ ports, and each port having an optical transceiver. All the optical transceivers are associated with the same wavelength λ₀. For each of the paired left node and right node, there is one and only one link between them, and thus, there are altogether N₁N₂ links in the interconnection network, as shown in FIG. 1, where the small block on each port of the node represents an optical transceiver.

An AWG-based modular interconnection network for reducing the cabling complexity of a data center mainly via the wavelength division multiplexing property of AWGs, comprises the following parameters:

N₁×N₂ AWG: having N₁ input ports, N₂ output ports, and being associated with a wavelength set Λ={λ₀, λ₁, . . . , λ_(N) ₁ ⁻¹}, as shown in FIG. 2;

N₂×N₂ AWG: having N₂ input ports, N₂ output ports, and being associated with a wavelength set Λ={λ₀, λ₁, . . . , λ_(N) ₂ ⁻¹};

N₁×1 wavelength multiplexer/demultiplexer: N₁×1 AWG;

N₂×1 wavelength multiplexer/demultiplexer: N₂×1 AWG;

n₁×1 wavelength multiplexer/demultiplexer: n₁×1 AWG;

n₂×1 wavelength multiplexer/demultiplexer: n₂×1 AWG;

N₁×N₂ AWG network S_(A)(n₁, r₁, n₁, n₂, r₂): a three-stage AWG network, which comprises N₁=r₁n₁ input ports on the input side, each input port being a 1×n₂ demultiplexer, N₂=r₂n₂ output ports on the output side, each output port being an n₁×1 multiplexer, and m_(A) r₁×r₂ AWGs on the central stage, where r₁=r₂=r, n₁=N₁/r, n₂=N₂/r, and m_(A)=n₁n₂, as shown in FIG. 3;

KN₂×N₂ AWG network S_(B)(K, N₂, K, 1, N₂): an AWG network, with K N₂×N₂ AWGs in the first stage, and N₂ K×1 multiplexers in the second stage, as shown in FIG. 4;

N₁×N₂ interconnection network

₂:N₁ left nodes and N₁ N₂×1 multiplexers on the left side, N₂ right nodes and N₂ 1×N₁ demultiplexers on the right side, and an N₁×N₂ AWG on the central stage;

N₁×N₂ interconnection network

_(A1): consists of N₁ left nodes and N₁ N₂×1 multiplexers, N₂ right nodes and N₂ 1×N₁ demultiplexers, and an N₁×N₂ AWG network S_(A) on the central stage, as shown in FIG. 3;

N₁×N₂ interconnection network

_(B1): consists of N₁ left nodes and N₁ N₂×1 multiplexers; N₂ right nodes and N₂ 1×N₁ demultiplexers, and an N₁×N₂ AWG network S_(B) on the central stage, as shown in FIG. 4;

N₁×N₂ interconnection network

_(A2): consists of N₁ left nodes and N₁n₂r×1 multiplexers, N₂ right nodes and N₂n₁1×r demultiplexers, and n₁n₂ identical r×r AWGs on the central stage, as shown in FIG. 5;

N₁×N₂ interconnection network

_(B2): consists of N₁ left nodes and N₁ N₂×1 multiplexers, N₂ right nodes and KN₂ 1×N₁ demultiplexers, and K identical N₂×N₂ AWGs on the central stage, as shown in FIG. 6.

A method of construction of an AWG-based modular interconnection network comprises the following steps:

(1) Remove all the N₁N₂ cables in the N₁×N₂ interconnection network

₁ as shown in FIG. 1, then provide N₁ N₂×1 wavelength multiplexers, labeled by L₀, L₁, . . . , L_(N) ₁ ⁻¹ for N₁ left nodes, the ith N₂×1 wavelength multiplexer having its jth input port connected with the jth port of the ith left node, and the jth port of the ith left node is associated with wavelength λ_([i+j]) _(N1) , where i=0, 1, . . . , N₁−1, and j=0, 1, . . . , N₂−1; provide N₂ 1×N₁ wavelength demultiplexers labeled by R₀, R₁, . . . , R_(N) ₂ -1, for N₂ right nodes, the jth 1×N₁ wavelength demultiplexer having its ith output port connected separately with the ith port of the jth right node, and the ith port of the jth right node is associated with wavelength λ_([i+r]) _(N1) . Use N₁×N₂ AWG to connect N₁ N₂×1 wavelength multiplexers on the left with N₂1×N₁ wavelength demultiplexers on the right. This step transforms the

₁ into an

₂, with all the optical fibers being replaced by an AWG, as shown in FIG. 2, where the ith left node connects with the jth right node through wavelength λ_([i+j]) _(N1) .

As the fabrication of AWGs with very large N₁ and N₂ is impractical, it is necessary to decompose the AWG into a network of small AWGs: substitute the N₁×N₂ AWG with an AWG network S_(A)(n₁,r₁,m_(A),n₂,r₂), as shown in FIG. 3. In S_(A), each input port is a 1×n₂ demultiplexer and the ith input port is labeled by D_(A1)(α_(A),a_(A)), where α_(A)=└i/n₁┘ and a_(A)=[i]_(n) ₁ , and each output port is a n₁×1 multiplexer and the jth output port is labeled by M_(A1)(β_(A),b_(A)), where β_(A)=└j/n₂┘, and b_(A)=[j]_(n) ₂ , and an AWG in the central stage is labeled by G_(A1)(a_(A),b_(A)); the α_(A)th port of G_(A1)(a_(A),b_(A)) is connected with the bath port of D_(A1)(α_(A),a_(A)), the β_(A)th port of G_(A1)(a_(A),b_(A)) is connected with the a_(A)th port of M_(A1)(β_(A),b_(A)), and G_(A1)(a_(A),b_(A)) is associated with a wavelength subset Λ_([a) _(A) _(+b) _(A) _(]) _(n1) ={λ_([a) _(A) _(+b) _(A) _(]) _(n1) _(r+k)|k=0, 1, . . . , r−1}. This step transforms

₂ to

_(A1), in which the ith left node connects with the jth right node via wavelength λ_([a) _(A) _(+b) _(A) _(]) _(n1) _(r+[α) _(A) _(+β) _(A) _(]) _(r) along the path as follows:

-   Left Node i→output b_(A) of D_(A1)(α_(A),a_(A))→input α_(A) of     G_(A1)(a_(A),b_(A))→output β_(A) of G_(A1)(a_(A),b_(A))→input a_(A)     of M_(A1)(β_(A),b_(A))→Right Node j.

As shown in FIG. 4, when N₁=KN₂, the three-stage network S_(A) degenerates into a two-stage network S_(B) (K,N₂,K,1,N₂), where each input port degenerates into a 1×1 demultiplexer, i.e., a fiber link, the dimension of the AWGs in the central stage is N₂×N₂, and each output port becomes a K×1 multiplexer. The ith input port is labeled by D_(B1)(α_(B),a_(B)), where α_(B)=└i/N₂┘, and a_(B)=[i]_(N) ₂ , the jth output port is labeled by M_(B1)(γ_(B)), where γ_(B)=j, and an AWG in the central stage is labeled by G_(B1)(α_(B)), and further, an AWG in the central stage is associated with a wavelength subset Λ_(α) _(B) ={λ_(α) _(B) _(N) ₂ _(+k)|k=0, 1, . . . , N₂−1}; the a_(B)th input port of G_(B1)(α_(B)) is thus D_(B1)(α_(B),a_(B)), and the γ_(B)th output port of G_(B1)(α_(H)) is connected with the α_(B)th input port of M_(B1)(γ_(B)). This step transforms

₂ into

_(B1), where the ith left node connects with the jth right node via wavelength λ_(α) _(B) _(N) ₂ _(+[α) _(B) _(+γ) _(B) _(]N) ₂ along the path as follows:

-   -   Left Node i→D_(B1)(α_(B),a_(B))→input a_(B) of         G_(B1)(α_(B))→output γ_(B) of G_(B1)(α_(B))→input α_(B) of         M_(B1)(γ_(B))→Right Node j.

Wavelengths are precious resources in an optical communication window, and the number of wavelengths required by the system should not increase with the dimension of the interconnection network, and therefore, wavelength reuse must be taken into account. As shown in FIG. 5, substitute the ith N₂×1 multiplexer L_(i) on the left side of

_(A1) and the 1×n₂ demultiplexer D_(B1)(α_(B),a_(B)) of S_(A) with n₂ r×1 multiplexers, each of which is labeled by D_(A2)(α_(A),a_(A),b_(A)), and substitute the jth 1×N₁ demultiplexer R_(j) on the right side of

_(A1) and the n₁×1 multiplexer M_(A1)(β_(A),b_(A)) of S_(A) with n₁ 1×r demultiplexers, each of which is labeled by M_(A1)(β_(A),b_(A),a_(A)). As the optical transceivers in the left and right nodes can perform wavelength isolation, each r×r AWG can reuse the same wavelength subset {λ_(k)|k=0, 1, . . . , r−1}. The r×r AWG in the central stage is labeled by G_(A2)(a_(A),b_(A)). The output port of D_(A2)(α_(A),a_(A),b_(A)) is connected with the α_(A)th input port of G_(A2)(a_(A),b_(A)), and the input port of M_(A2)(β_(A),b_(A),a_(A)) is connected with the β_(A)th output port of G_(A2)(a_(A),b_(A)). Accordingly

_(A1) is transformed into

_(A2), where the ith left node connects with the jth right node via wavelength λ_([λα) _(A) _(+β) _(A) _(]) _(r) , along the path as follows:

-   -   Left Node i→D_(A2)(α_(A),a_(A),b_(A))→input α_(A) of         G_(A2)(α_(A),b_(A))→output β_(A) of         G_(A2)(a_(A),b_(A))→M_(A1)(β_(A),b_(A),a_(A))→Right Node j.

As shown in FIG. 6, if the outcome of step (2) is

_(B1), substitute the ith 1×N₁ demultiplexer R_(j) on the right side of

_(B1) and the jth K×1 multiplexer M_(B1)(γ_(B)) on the output side of S_(B) with K N₂×1 demultiplexers, each of which is labeled by M_(B2)(γ_(B),α_(B)). Each N₂×N₂ AWG in the central stage is labeled by G_(B2)(α_(B)) and can be associated with the same wavelength subset {λ_(k)|k=0, 1, . . . , N₂−1}. The input port is labeled by D_(B2)(α_(B),a_(B)). D_(B2)(α_(B),a_(B)) is connected with the a_(B)th input port of G_(B2)(α_(B)), and M_(B2)(γ_(B),α_(B)) is connected with the γ_(B)th output port of G_(B2)(α_(B)). As a result,

_(B1) is transformed into

_(B2), in which the ith left node connects with the jth right node via wavelength λ_([α) _(B) _(+γ) _(B) _(]N) ₂ along the path as follows:

-   Left Node i→D_(B2)(α_(B),a_(B))→input a_(B) of G_(B2)(α_(B))→output     γ_(B) of G_(B2)(α_(B))→M_(B2)(γ_(B),α_(B))→Right Node j.

(2) If the dimension of the AWG in the central stage is still very large, the method of step (2) can be employed to substitute each AWG in the central stage with a module encapsulated with a three-stage AWG network.

Example 1

A method for constructing an AWG-based modular interconnection network is shown. As for a 15×10 interconnection network

₁, as shown in FIG. 7, where the greatest common divisor of 15 and 10 is 5, the construction method of an AWG-based modular interconnection network comprises the following steps:

1. Substitute the 150 cables on FIG. 7 with a 15×10 AWG, which is associated with Λ={λ₀, λ₁, . . . , λ₁₄).

₁ is thus transformed into

₂. Compared with

₁,

₂ does not need optical fiber links, as shown in FIG. 8;

2. Decompose the 15×10 AWG in

₂ into an AWG network S_(A)(3,5,6,2,5), which consists of fifteen (15) 1×2 demultiplexers, six (6) 5×5 AWGs, and ten (10) 3×1 multiplexers. Accordingly, the wavelength set Λ=(λ₀, λ₁, . . . , λ₁₄} is divided to 3 subsets Λ₀={λ₀, . . . , λ₄}, Λ₁={λ₅, . . . , λ₉}, and Λ₂={λ₁₀, . . . , λ₁₄}, which are respectively associated with the six (6) 5×5 AWGs in the central stage. As shown in FIG. 9, this step transforms

₂ into

_(A1). Compared with the 150 optical fiber links of

₁,

_(A1) needs only 60 optical fiber links. The reduction ratio of the number of required optical fiber links in this example is 2.5;

3. Substitute a 1×2 demultiplexer of S_(A) and a 10×1 multiplexer on the left side of

₂ with two (2) 5×1 AWGs, and substitute a 3×1 multiplexer of S_(A) and the 1×15 demultiplexer on the right side of

₂ with three (3) 1×5 AWG Wavelength dependence among the 6 5×5 AWGs is eliminated due to the transceivers equipped on both sides of

₂. Thus, these AWGs can be associated with the same wavelength subset Λ₀, which indicates that the wavelength reuse property is achieved. As shown in FIG. 10, an AWG-based modular interconnection network

₂ is obtained. The number of required optical fibers in

_(A2) is 60. After the construction of an AWG-based modular interconnection network, the number of optical fiber links is reduced from 150 to 60, and the reduction of the number of optical fiber links remarkably cuts down the network complexity and thus simplifies system maintenance. In general, the number of optical fiber links is reduced r/2 times. In practical applications, N₁ and N₂ might be very large, which results in that the dimension of the AWGs in the central stage is still large. In this case, the method in step (2) can be employed to substitute each AWG in the central stage with a module that consists of a three-stage network of small AWGs.

Example 2

A method for constructing an AWG-based modular interconnection network, as for a 12×6 interconnection network

₁ as shown in FIG. 11, where 12 is a multiple of 6, the construction comprises the following steps:

1. Substitute the 72 linking cables in the middle of FIG. 11 with a 12×6 AWG, which is associated with Λ={λ₀, λ₁, . . . , λ₁₁}. This operation transforms

₁ to

₂. Compared with

₁,

₂ does not need optical fiber links, as shown in FIG. 12.

2. Decompose the 12×6 AWG in N₂ into an AWG network S_(B)(2,6,2,1,6) that consists of six (6) 1×2 multiplexers, two (2) 6×6 AWGs. Accordingly, Λ={λ₀, λ₁, . . . , λ₁₄} is divided into 2 subsets Λ₀={λ₀, . . . , λ₅} and Λ₁={λ₆, . . . , λ₁₁}, which are respectively associated with the two (2) 6×6 AWGs in the central stage. As shown in FIG. 13, this step transforms into

₂ Compared with the optical fiber links of

₁,

_(B1) needs only 12 optical fiber links. The reduction ratio of the number of optical fiber links in this example is 6.

3. Substitute a 2×1 multiplexer of S_(B) and a 1×12 demultiplexer on the right side of

₂ with two (2) 1×6 AWGs. Wavelength dependence between the two (2) 6×6 AWGs is eliminated due to the transceivers provided on both sides of

₂. Thus, these AWGs can be associated with the same wavelength subset Λ₀, which indicates that the wavelength reuse property is achieved. As shown in FIG. 14, an AWG-based modular interconnection network

_(B2) is obtained. The number of required optical fibers in

_(B2) is 12. In practical applications, N₁ and N₂ might become very large, resulting in large AWGs in the central stage. In such a case, the method in step (2) can be employed to substitute the AWG in the central stage with a module that consists of a three-stage network of small AWGs. This is the idea of modulization of the present invention. After the construction of an AWG-based modular interconnection network, the number of optical fiber links is reduced from 72 to 12, a 6 time reduction. General speaking, when N₁ is a multiple of N₂, the number of optical fiber links can be reduced from N₁N₂ to N₁, by employing the method. The reduction of the number of optical fiber links cuts down the network complexity and thus simplifies network maintenance. 

We claim:
 1. A method for constructing an interconnection network, comprising: providing N₁ N₂×1 wavelength multiplexers, labeled by L₀, L₁, . . . , L_(N) _(_) ⁻¹, for N₁ left nodes, an ith N₂×1 wavelength multiplexer having its jth input port connected with a jth port of an ith left node, and a jth port of the ith left node is associated with a wavelength λ_([i + j]_(N₁)), wherein i=0, 1, . . . , N₁−1, j=0, 1, . . . , N₂−1; providing N₂ 1×N₁ wavelength demultiplexers labeled by R₀, R₁, . . . , R_(N) ₂ −₁, for N₂ right nodes, a jth 1×N₁ wavelength demultiplexer having its ith output port connected separately with an ith port of a jth right node, and an ith port of a jth right node is associated with wavelength λ_([i + j]_(N₁)); interconnecting the N₁ wavelength multiplexers on the left with the N₂ wavelength demultiplexers on the right via the N₁×N₂ AWG, the N₁×N₂ AWG having the N₁ input ports and the N₂ output ports, and being associated with the wavelength set Λ={λ₀, λ₁, . . . , λ_(N) ₁ ⁻¹}; decomposing the N₁×N₂ AWG to a three-stage AWG network S_(A)(n₁, r₁, m_(A), n₂, r₂), wherein the AWG network S_(A) comprises N₁=r₁n₁ input ports on an input side, with each input port being a 1×n₂ wavelength demultiplexer, and N₂=r₂n₂ output ports on an output side, with each output port being an n₁×1 wavelength multiplexer, m_(A) r₁×r₂AWGs in the central stage, wherein r₁=r₂=r, n₁=N₁/r, n₂=N₂/r, and m_(A)=n₁n₂; an ith input port is labeled by D_(A1)(α_(A), a_(A)), wherein α_(A)=└i/n₁┘ and a_(A)=[i]_(n) ₂ , and a jth output port is labeled by M_(A1)(β_(A), b_(A)), wherein β_(A)=└j/n₂┘ and b_(A)=[j]_(n) ₂ , and each of the AWGs in the central stage is labeled by G_(A1)(α_(A), b_(A)); the α_(A)th input port of G_(A1)(α_(A), b_(A)) is connected with the b_(A)th output port of D_(A1)(α_(A), a_(A)), the β_(A)th output port of G_(A1)(α_(A), b_(A)) is connected with the α_(A)th input port of M_(A1)(β_(A), b_(A)), and G_(A1)(α_(A), b_(A)) is associated with a wavelength subset Λ_([a_(A) + b_(A)]_(n₁)) = {λ_([a_(A) + b_(A)]_(n₁)r + k)|k = 0, 1, …  , r − 1}; replacing the ith N₂×1 wavelength multiplexer L_(i) and the 1×n₂ wavelength demultiplexer D_(A1)(α_(A), a_(A)) with n₂ r×1 wavelength multiplexers, each of the r×1 wavelength multiplexers is labeled by D_(A2)(α_(A), a_(A), b_(A)); replacing the jth 1×N₁ wavelength demultiplexer R_(j) and the n₁×1 wavelength multiplexer M_(A1)(β_(A), b_(A)) with n₁ r×1 wavelength demultiplexers, each of the r×1 wavelength demultiplexers being labeled by M_(A2)(β_(A), b_(A), α_(A)); and associating each r₁×r₂ AWG, labeled by G_(A2)(α_(A), b_(A)), with a wavelength subset {λ_(k)|k=0, 1, . . . , r−1}; wherein the output port of D_(A2)(α_(A), a_(A), b_(A)) is connected with the α_(A)th input port of G_(A2)(α_(A),b_(A)), and the input port of M_(A2)(β_(A), b_(A), α_(A)) is connected with the β_(A)th output port of G_(A2)(α_(A), b_(A)).
 2. An AWG-based modular interconnection network according to claim 1, comprising: left nodes, a number of the left nodes being N₁, and each of the left nodes having N₂ ports, right nodes, a number of the right nodes being N₂, and each of the right nodes having N₁ ports, an optical transceiver associated with a fixed wavelength on each port of the left and right nodes, r×1 wavelength multiplexers, a number of the r×1 wavelength multiplexers being N₁n₂, each of the n₂ r×1 wavelength multiplexers having N₂ input ports being connected with the N₂ ports of one of the left nodes, and n₂=N₂/r, 1×r wavelength demultiplexers, a number of the 1×r wavelength demultiplexers being N₂n₁, each of the n₁ 1×r wavelength demultiplexers having N₁ output ports being connected with the N₁ ports of one of the right nodes, and n₁=N₁/r, and r×r AWGs connecting the r×1 wavelength multiplexers and the 1×r wavelength demultiplexer, a number of the r×r AWGs being n₁n₂, each of the r×r AWGs being associated with a wavelength subset {λ_(k)|k=0, 1, . . . , r−1}, where N₁≧N₂, N₁ and N₂ are integers that have a greatest common divisor r, and r>1.
 3. The method as claimed in claim 1, further comprising: replacing the AWG in the central stage with a module constituted of a network AWG of three stages.
 4. A method for constructing an interconnection network, comprising: providing N₁ N₂×1 wavelength multiplexers, labeled by L₀, L₁, . . . , L_(N) ₁ ⁻¹, for N₁ left nodes, an ith N₂×1 wavelength multiplexer having its ith input port connected with a jth port of an ith left node, and a jth port of the ith left node is associated with a wavelength λ_([i + j]_(N₁)), wherein i=0, 1, . . . , N₁−1, j=0, 1, . . . , N₂−1, and N₁=KN₂; providing N₂ 1×N₁ wavelength demultiplexers labeled by R₀, R₁, . . . , R_(N) ₂ ⁻¹, for N₂ right nodes, a jth 1×N₁ wavelength demultiplexer having its ith output port connected separately with an ith port of a jth right node, and an ith port of a jth right node is associated with wavelength λ_([i + j]_(N₁)); interconnecting the N₁ wavelength multiplexers on the left with the N₂ wavelength demultiplexers on the right via the N₁×N₂ AWG, the N₁×N₂ AWG having the N₁ input ports and the N₂ output ports, and being associated with the wavelength set A={λ₀, λ₁, . . . , λ_(N) ₁ ⁻¹}; decomposing the N₁×N₂ AWG to a two-stage network S_(B)(K, N₂, K, 1, N₂), wherein each input port of the AWG network S_(B) is a link, there are K N₂×N₂ AWGs in the central stage, and each output port is a K×1 wavelength multiplexer; the ith input port is labeled by D_(B1)(α_(B),a_(B)), wherein α_(B)=└i/N₂┘ and a_(B)=[i]_(N) ₂ , the jth output port is labeled by M_(B1)(γ_(B)), wherein γ_(B)=j, and each AWG in the central stage is labeled by G_(B1)(α_(B)), and the AWG in the central stage is associated with a wavelength subset Λ_(α) _(B) ={λ_(α) _(B) _(N) ₂ _(+k)|k=0, 1, . . . , N₂−1}; the α_(B)th input port of G_(B1)(α_(B)) is thus D_(B1)(α_(B), a_(B)), the γ_(B)th output port of G_(B1)(α_(B)) is connected with the α_(B)th input port of M_(B1)(γ_(B)); denoting each of the N₁×1 wavelength multiplexers as D_(B2) (α₁, a_(B)); replacing the jth 1×N₁ demultiplexer R_(j) and the K×1 multiplexer M_(B1)(γ_(B)) with K N₂×1 wavelength multiplexers, each of the N₂×1 wavelength multiplexers being labeled by M_(B2)(γ_(B),α_(B)); and associating each N₂×N₂ AWG, labeled by G_(B2)(α_(B)), with a wavelength subset {λ_(k)|k=0, 1, . . . , N₂−1}; wherein D₂(a_(B),a_(B)) is connected with the α_(B)th input port of G_(B2)(α_(B)), and M_(B2)(γ_(B),α_(B)) is connected with the γ_(B)th output port of G_(B2)(α_(B)).
 5. An AWG-based modular interconnection network according to claim 4, comprising: left nodes, a number of the left nodes being N₁, and each of the left nodes having N₂ ports, right nodes, a number of the right nodes being N₂, and each of the right nodes having N₁ ports, an optical transceiver associated with a fixed wavelength on each port of the left or right node, N₂×1 wavelength multiplexers, a number of the N₂×1 wavelength multiplexers being N₁, and each of the N₂×1 wavelength multiplexers having N₂ input ports being connected with the N₂ ports of one of the left nodes; 1×N₂ wavelength demultiplexers, a number of the 1×N_(z) wavelength demultiplexers being N₁=KN₂, and each of the K 1×N₂ wavelength demultiplexers having N₁ output ports being connected with the N₁ ports of one of the right nodes; and N₂×N₂ AWGs connecting the N₂×1 wavelength multiplexers and the 1×N₂ wavelength demultiplexers, a number of the N₂×N₂ AWGs being K, and each of the N₂×N₂ AWGs being associated with a wavelength subset {λ_(i)|i=0, 1, . . . , N₂−1}, wherein N₁=KN₂.
 6. The method as claimed in claim 4, further comprising: replacing the AWG in the central stage with a module constituted of a three-stage network of AWGs. 